动点的牵连运动分析与运动合成定理推证

点的合成运动分析中,复杂运动合理地分解和合成的关键在于牵连点的运动分析,牵连点是动系上与动点瞬时相重合的点,由于动点在动系上不断变迁,故牵连点随时间变动。本文指出,任一瞬时,牵连点均是动系上的某一“固定”点,仅随动系一起运动,采用解析方法提出了牵连点速度和加速度的一种表示方法,并推导了点的速度和加速度合成定理。本方法无需引入相对导数,易于学生理解。

ANALYSIS ON THE TRANSPORT MOTION AND PROOF OF THE COMPOSITION THEOREM FOR MOVING POINTS

In the analysis of composite motion for points, the kinematic analysis of the transport point is the key for decomposing or synthesizing the motion of moving point. The transport point is the point on the moving coordinate system that coincides with the moving point instantaneously. In this paper, it is pointed out that at any time, the transport point is a “fixed” point on the moving coordinate system and it only moves with the moving coordinate system. This paper presents an analytic method of expressing velocity and acceleration of transport point, and it also derives the synthesis theorem of velocity and acceleration of moving point. This method does not need to introduce the relative derivative, hence it avoids the difficulty within the derivation method of displacement or relative derivative, which is hard to understand for students.